Criteria and Topics for the 2018 Doctoral Studies Admission, Mathematics

approved by the Faculty Council on 06.02.2018

The admission exam consists of

A written exam based on topics from the thematic area selected by the candidate.

An interview in which the scientific interests of the candidate, as well as the research topic proposed for the PhD thesis are analyzed.

The candidates will be admitted, based on their options and admission scores, on the available state budgeted places (full-time and part-time). The admission score is computed as follows:

40% the grade for the written exam;

40% the grade for the interview;

20% the average grade of promoting the years of study at the Master level/Advanced Studies or the average grade of promoting the years of study at the Bachelor level for the graduates of the long-time higher education studies from the period prior to the application of the three Bologna cycles (which do not have a Master diploma). In the case of equal admission scores, the grade from the written exam will be considered for ranking.

For admission to the doctoral studies, the admission score must be at least 7 (seven).

Topics in Analysis

Differentiability of real and vector functions of vector variables: the Fréchet differential, necessary and sufficient conditions of differentiability; relation between differentiability and continuity; partial derivatives, representation of the differential by partial derivatives, derivatives and differentials of higher order, Taylor’s formula;

Linear and continuous operators between normed spaces: characterizations of continuity of linear operators between normed spaces; the open mapping theorem, the closed graphs theorem, the normed space of linear and continuous operators between normed spaces

The theory of viscous Newtonian fluid: The constitutive equation and the Navier-Stokes equations. Special forms of the Navier-Stokes equations. The Stokes system. The fundamental solution of the Stokes system. Uniqueness theorems for the Dirichlet problem for the Stokes system.